Sensors that can determine thermal quantities such as the thermal conductivity belong already to the state of the art. Most of them determine the thermal properties with the help of analytical models or equivalent electrical circuit thermal models. This is described for example by J. Kuntner, F. Kohl, and B. Jakoby, “Simultaneous thermal conductivity and diffusivity sensing in liquids using a micromachined device,” Sensors Actuators, A Phys., vol. 130-131, no. SPEC. ISS., pp. 62-67, August 2006.
Reduced order models were so far used for different reasons. Different reduced order model methods have been developed and a classification of them was made by T. Antoulas, “Model reduction of large-scale systems Lecture I: Overview Balanced truncation Krylov methods Moment matching,” 2008.
They can be classified in two main categories, these are the Krylov-based methods and the SVD-based (Singular Value Decomposition) methods. The reduction process starts with the finite element method (FEM) model that is a high order model and needs high computational effort. This is the advantage of a reduced order model (ROM) against the high order model (FEM model), as ROM can be solved much faster than the high order model, due to its significantly lower dimensions.
The reduced order modeling methods are mainly used for system simulation, control and design. One significant application fields constitutes the structural dynamics. Reduced order modeling approach for thermals system has been presented by C. Moosmann, E. B. Rudnyi, A. Greiner, and J. G. Korvink, “Model Order Reduction for Linear Convective Thermal Flow,” no. April, pp. 1-9, 2004 for the simulation of a micro thermal flow meter.
In addition, U. Baur, P. Benner, A. Greiner, J. Korvink, J. Lienemann, and C. Moosmann, “Parameter pre-serving model order reduction for MEMS applications,” Mathematical and Computer Modeling of Dynamical Systems, vol. 17, pp. 297-317, August 2011 also used parametric reduced order model for micro-thermal flow meter.